On the Recurrence of Birkhoff Sums for a Circle Rotation and a Hölder Function

We consider a zero-mean Hölder function on the circle. If an irrational rotation of the circle is sufficiently well approximable by rational rotations, then the sequence of values of the Birkhoff sums remains finite at each point of the circle.

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Publication Details

Journal
Theory of Probability and Its Applications
Published
2026-02-01
DOI
https://doi.org/10.1137/s0040585x97t992628
Primary Topic
Mathematical Dynamics and Fractals
Type
article
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article

On the Recurrence of Birkhoff Sums for a Circle Rotation and a Hölder Function

A. V. Kochergin
Theory of Probability and Its Applications
Mathematical Dynamics and Fractals
article

On the Recurrence of Birkhoff Sums for a Circle Rotation and a Hölder Function

A. V. Kochergin
article en

Abstract

We consider a zero-mean Hölder function on the circle. If an irrational rotation of the circle is sufficiently well approximable by rational rotations, then the sequence of values of the Birkhoff sums remains finite at each point of the circle.

Theory of Probability and Its ApplicationsVol. 70(4)
Reduced inequalities
Openalex Percentile: Top 45%
Mathematical Dynamics and Fractals
DOISourceOpenAlex
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On the Recurrence of Birkhoff Sums for a Circle Rotation and a Hölder Function — A. V. Kochergin · Theory of Probability and Its Applications (2026) | TGRS Research Map | TGRS